Infrared and Raman spectra, conformational stability, ab initio calculations and vibrational assignment of 1-hexen-4-yne

Article abstract of DOI:10.1039/b301450a

The infrared spectra (3500-50 cm^-1) of the gas and solid and the Raman spectra (3500-50 cm^-1) of the liquid and solid have been recorded for 1-hexen-4-yne, CH₂=CHCH₂C≡CCH₃. Also variable temperature studies over the temperature range -105 to -150°C of the infrared spectra (3500-400 cm^-1) of the sample dissolved in liquid krypton have been carried out. By utilizing these data from seven cis/gauche conformer pairs, the cis conformer is found to be the lower energy form with an enthalpy difference of 233 ± 23 cm^-1 (2.79 ± 0.28 kJ mol^-1). At room temperature it is estimated that there is 39 ± 2% of the gauche conformer present. Equilibrium geometries and energies of the two conformers have been predicted from ab initio calculations by perturbation theory (MP2) with full electron correlation to second order and hybrid density functional theory (DFT) calculations by the B3LYP method with a number of basis sets. A complete vibrational assignment is proposed for the cis conformer based on the vibrational-rotational band contours, relative intensities, Raman depolarization ratios and predicted frequencies from the ab initio and DFT calculations and many of the fundamentals for the gauche form have been assigned. The observation of sub-band structure for two of the nearly degenerate methyl vibrations indicates that the CH₃ group has almost free internal rotation which is consistent with the ab initio predicted barrier of 100 cm^-1. From the spacings of the sub-bands the values of the Coriolis coupling constants, ζ, have been determined for the CH₃ stretch and deformation.

Full text of DOI:10.1039/b301450a

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Infrared and Raman spectra, conformational stability, ab initio
calculations and vibrational assignment of 1-hexen-4-yney
b
Gamil A. Guirgis,a Xiaodong Zhu,z Frederick J. Heldrich,a Matthew J. Wrighta and
James R. Durig*b
a
Department of Chemistry & Biochemistry, College of Charleston, Charleston, SC 29403, USA
Department of Chemistry, University of Missouri-Kansas City, Kansas City, MO 64110-2499,
USA. E-mail: durigj@umkc.edu; Fax: 01 816-235-2290; Tel: 01 816-235-6038
b
Received 5th February 2003, Accepted 25th April 2003
First published as an Advance Article on the web 14th May 2003
The infrared spectra (3500–50 cmꢀ1) of the gas and solid and the Raman spectra (3500–50 cmꢀ1) of the liquid
=
=
=
and solid have been recorded for 1-hexen-4-yne, CH2 CHCH C CCH . Also variable temperature studies
2
3
over the temperature range ꢀ105 to ꢀ150 ꢁC of the infrared spectra (3500–400 cmꢀ1) of the sample dissolved in
liquid krypton have been carried out. By utilizing these data from seven cis/gauche conformer pairs, the cis
conformer is found to be the lower energy form with an enthalpy difference of 233 ꢂ 23 cmꢀ1 (2.79 ꢂ 0.28 kJ
molꢀ1). At room temperature it is estimated that there is 39 ꢂ 2% of the gauche conformer present. Equilibrium
geometries and energies of the two conformers have been predicted from ab initio calculations by perturbation
theory (MP2) with full electron correlation to second order and hybrid density functional theory (DFT)
calculations by the B3LYP method with a number of basis sets. A complete vibrational assignment is proposed
for the cis conformer based on the vibrational-rotational band contours, relative intensities, Raman
depolarization ratios and predicted frequencies from the ab initio and DFT calculations and many of the
fundamentals for the gauche form have been assigned. The observation of sub-band structure for two of the
nearly degenerate methyl vibrations indicates that the CH3 group has almost free internal rotation which
is consistent with the ab initio predicted barrier of 100 cmꢀ1. From the spacings of the sub-bands the values
of the Coriolis coupling constants, z, have been determined for the CH3 stretch and deformation.
but now with the cis conformer being more stable. In order to
Introduction
continue our investigation on conformational stability of
substituted propenes with another unsaturated substituted
group, we initiated a vibrational spectroscopic and theoretical
investigation of the conformational stability of 1-hexen-4-yne,
The structural parameters, conformational stability, and vibra-
=
tional spectra of the 3-monosubstituted propenes, CH2
CHCH2X, where X ¼ F,1,2 Cl,3 Br,4,5 I,6 CN,7 CH3 ,8 SiH3 ,9
16
NH2 ,10–13 OH,14,15 C CH, etc. have been of interest for
=
=
=
=
CH2 CHCH C CCH .y
=
2
3
many years. For the allyl halides only the fluoride has the cis con-
former as the more stable rotamer, but many of the ab initio
calculations2 at the MP2 level with full electron correlation
with relatively large basis sets with diffuse functions predict
the gauche conformer as the more stable form. Similar pro-
blems also exist for the prediction of the conformational stabi-
lity of 1-butene8 (X ¼ CH3). Therefore, the steric hindrance
appears to dominate the conformational behavior of these
molecules where the substituents X are saturated moieties.
There have been no previous spectroscopic studies reported
for 1-hexen-4-yne, and we, therefore, recorded the Raman
spectra of the liquid and solid along with the infrared spectra
of the gas, krypton solutions with variable temperatures, and
the solid. We have also carried out ab initio calculations
employing the 6-31G(d) basis set at the level of restricted
Hartree–Fock (RHF) and with the Møller–Plesset perturba-
tion method (MP2) to second order to obtain equilibrium geo-
metries, force constants, vibrational frequencies, infrared and
Raman intensities, and conformational stabilities. Structural
parameters and conformational stabilities have also been
obtained from calculations with larger basis sets of 6-
311G(d, p) and 6-311G(2d, 2p) without diffuse functions at
the MP2 level with full electron correlation. Hybrid density
functional theory DFT calculations by the B3LYP method
with a variety of basis sets have also been carried out. The
results of these spectroscopic and theoretical studies are
reported herein.
However, 3-cyanopropene,7 CH2 CHCH2CN, where the
=
experimental enthalpy difference is 336 cmꢀ1, shows that the
cis conformer is the more stable form. For another similar
molecule, 1-penten-4-yne,16 the MP2/6-311+G(d, p) calcula-
tions predict the gauche form to be more stable by 13 cmꢀ1
which is not consistent with the experimental result of an
enthalpy difference of 248 cmꢀ1 with the cis rotamer being
more stable. However by utilizing a larger basis set 6-
311+G(2d, 2p), a much larger value of 183 cmꢀ1 is determined
y Electronic supplementary information (ESI) available: IR and
Raman data (Table S1) and symmetry coordinates for vibrations
(Table S2) of 1-hexene-4-yne. See http://www.rsc.org/suppdata/cp/
b3/b301450a/
z Taken in part from the thesis of X. Zhu which will be submitted to
the Department of Chemistry at the University of Missouri-Kansas
City in partial fulfillment of the PhD degree.
Experimental
All chemicals used in the preparations were obtained from
Aldrich Chem. Co., Milwaukee, WI. The compound 1-hexen-
4-yne was prepared by the previously reported method with
modification.17 A multiple neck, 1 L, round bottom flask,
DOI: 10.1039/b301450a
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551
This journal is # The Owner Societies 2003
2541

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fitted with a condenser, septum, and magnetic stir bar was
flame dried under positive Ar. To the flask was added 800
mL (0.40 mole) of commercially available propynyl magne-
sium bromide (0.5 M in THF) and 3.90 g (0.19 mole) of
CuBrꢃdimethyl sulfide. The suspension was stirred and 30
mL (0.35 mole) of allyl bromide was added by syringe. The
reaction gradually became warm, and then an additional 1
ml of allyl bromide (0.012 mole) was added and the reaction
was heated to reflux with stirring for one hour and then left
to stir overnight at room temperature under positive Ar. The
resulting thick slurry was treated with 2 M HCl (1.1 L) and
extracted with DECALIN&#61666. The combined DECA-
LIN&#61666 extracts were washed with brine and water and
analyzed by headspace GC-MS to monitor THF removal:
washings of brine following with water. The organic layer
was dried (Na2SO4), and fractionally distilled through a 10
cm column of glass Raschig rings to yield the product (BP
85–86 ꢁC) with 50% yield. The structure of the compound
was confirmed by infrared, mass spectrometry and 1H and
13C nuclear magnetic resonance. Routine MS data recorded
on a Hewlett-Packard 5971 MSD; m/z (rel. int.): 81(6.7),
80(100%), 79(99.7), 77(85.1), 53(20.3), 52(22.0), 51(23.8). Rou-
tine 1H NMR recorded in CDCl3 at 300 MHz on a Varian
Mercury system; ppm (m, J, #H): 5.79 (m, 1HC2H), 5.28(d
of q, Jtrans ¼ 17 Hz, J ¼ 1.8 Hz, 1HC1H), 5.06 (d of q,
Jcis ¼ 10 Hz, J ¼ 1.6 Hz, 1HC1H), 2.90 (m, 2HC3H), 1.81 (t,
J ¼ 2.5 Hz, 3HC6H). Routine 13C NMR recorded at 75
MHz on a Varian Mercury system; ppm: 133.5 (C2), 115.8
(C1), 77.2, 76.0, 23.5 (C3), 3.85 (C6). Of particular note in
the characterization of 1-hexen-4-yne was the extensive cou-
pling observed in the gCOSY spectrum and the identification
of 13C signal from HETCOR data. The gCOSY revealed cou-
pling between all expected vicinal positions and weak longer-
range coupling was manifested from the methylene protons
at C3 to the methyl protons at C6 (5 bond). HETCOR data
secured assignments of C1 and C2 in the 13C data, with correla-
tion of 13C signals at 133.5 ppm (C2) to 1H signal at 5.79 ppm
(C2), and 13C signal at 115.8 ppm (C1) to two olefinic reso-
nances of C1 at 5.28 and 5.06 ppm. Further purification of
the sample was performed using a low temperature, low-pres-
sure fractionating column and the sample was collected at
ꢀ60 ꢁC at 150 mT. The sample was stored under vacuum at
low temperature.
The mid-infrared spectrum of the gas (Fig. 1A) was recorded
on a Perkin-Elmer model 2000 Fourier transform spectrometer
equipped with a Ge/CsI beamsplitter and DTGS detector.
Atmospheric water vapor was removed from the spectrometer
housing by purging with dry nitrogen. The spectrum of the gas
was obtained using a 10 cm cell fitted with CsI windows. The
infrared spectrum of the solid (Fig. 1B) was obtained by con-
densing the sample on a CsI substrate held at the temperature
of boiling liquid nitrogen, housed in a vacuum cell fitted with a
CsI window. The sample was condensed as an amorphous or
glassy solid and repeatedly annealed until no further changes
were observed in the spectrum.
The mid-infrared spectra of the sample dissolved in liquid
krypton (Fig. 2A) as a function of temperature were recorded
on the Bruker model ISF 66 Fourier transform spectrometer
equipped with a globar source, a Ge/KBr beamsplitter and a
TGS detector. In all case 100 interferograms were collected
at 1.0 cmꢀ1 resolution, averaged and transformed with a box-
car truncation function. A specially designed cryostat cell was
used to obtain the spectral data. It consists of a copper cell
with a path length of 4 cm with wedged silicon window sealed
to the cell with indium gaskets. This cell was cooled by boiling
liquid nitrogen and the temperature was monitored with two
Pt thermoresistors. The complete cell was connected to a pres-
sure manifold which allows the filling and evacuation of the
cell. After the cell had cooled to the designated temperature,
a small amount of the compound was condensed into the cell.
Next, the pressure manifold and the cell were pressurized with
the noble gas, which immediately started to condense in the
cell, allowing the compound to dissolve.
The far infrared spectrum of the gas (Fig. 3) was recorded
on a Bomem model DA3.002 Fourier transform spectrometer
equipped with a vacuum bench, 6.25 and 25 mm Mylar beam
splitters, and a liquid helium-cooled Si bolometer. The
Fig. 2 Mid-infrared spectra of 1-hexen-4-yne: (A) krypton solution
at ꢀ125 ꢁC; (B) simulated infrared spectrum of the cis and gauche con-
former mixture with the DH of 233 cmꢀ1; (C) calculated spectrum of
the pure gauche conformer; and (D) calculated spectrum of the pure
cis conformer.
Fig. 1 Mid-infrared spectra of 1-hexen-4-yne in: (A) gas; and (B)
polycrystalline solid.
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were checked by measuring the state of polarization of the
Raman bands of carbon tetrachloride immediately before
depolarization measurements were made on the liquid samples.
The Raman frequencies are expected to be accurate to ꢂ2
cmꢀ1 and typical spectra are shown in Fig. 4. The wavenum-
bers for all of the observed bands by the different techniques
in the various physical states are listed in Table S1.y
Ab initio calculations
The electronic structure calculations were performed with the
Gaussian 98 program19 with Gaussian type basis functions.
The energies of 1-hexen-4-yne were obtained from calculations
at the restricted Hartree–Fock (RHF) level and Møller–Plesset
perturbation theory20 at the second order (MP2) with basis
sets 6-31G(d), 6-311G(d,p) and 6-311G(2d,2p) and from
hybrid density function theory (DFT) calculations by the
B3LYP method and the results are given in Table 1. The
gauche conformer is predicted to be the lower energy form
by RHF calculations. However, the cis conformer is predicted
to be more stable by MP2 and B3LYP calculations irrespective
of the basis set with the energy differences ranging from 47 to
242 cmꢀ1. Therefore, it was necessary to utilize the experimen-
tal data to confidently determine the conformational stability.
The optimized values of the structural parameters obtained
by ab initio calculations are given in Table 2 for both the
cis and gauche forms. The Gaussian 98 program19 was also
employed in calculating the force field in Cartesian coordinates
by each of the computational methods. In order to obtain a
complete assignment of the vibrational modes for 1-hexen-4-
yne, the internal coordinates defined in Table 2 and shown
in Fig. 5 were used to form the symmetry coordinates listed
in Table S2.y The B-matrix elements were used to convert
the ab initio calculated force field from Cartesian coordinates
into the force field in internal coordinates.21 These force con-
stants were used in a mass-weighted Cartesian coordinate
calculation to reproduce the ab initio predicted frequencies
and to determine the potential energy distributions (P.E.D.),
which are given in Table 3 for both cis and gauche conformers.
The diagonal and off-diagonal elements of the force field in the
internal coordinates were then modified with scaling factors of
0.88 for the carbon–hydrogen stretches, 0.9 for the heavy atom
stretches and carbon hydrogen bends, 1.0 for the skeletal
Fig. 3 Far-infrared spectra of 1-hexen-4-yne: (A) gas; (B) amorphous
solid and (C) polycrystalline solid.
spectrum was obtained from the sample contained in a 1 m
folded path cell equipped with mirrors coated with gold, and
fitted with polyethylene windows with an effective resolution
of 0.1 cmꢀ1. The far-infrared spectra of the amorphous and
crystalline solids (Fig. 3) were obtained with the Perkin-Elmer
model 2000 equipped with a metal grid beamsplitter and a
DTGS detector.
The Raman spectra (Fig. 4) were recorded on a SPEX
model 1403 spectrophotometer equipped with a Spectra-
Physics model 164 argon ion laser operating on the 514.5 nm
line. The laser power used was 0.5 W with a spectral bandpass
of 3 cmꢀ1. The spectra of the liquid and solid were recorded
with the sample sealed in a Pyrex glass capillary. The annealed
polycrystalline solid was recorded with the capillary cooled by
cold nitrogen gas.18 Depolarization ratio measurements were
obtained for the liquid sample using a standard Ednalite 35
mm camera polarizer with a 38 mm free aperture affixed to
the SPEX instrument. Depolarization ratio measurements
=
bends except the C CC bends which are scaled by a factor
=
of 1.3. The calculations were repeated to obtain the fixed
scaled force fields and scaled vibrational frequencies.
Infrared intensities were calculated based on the dipole
moment derivatives with respect to the Cartesian coordinates.
The derivatives were taken from the ab initio calculations
Table 1 Calculated energies and energy differences for cis and gauche
conformers of 1-hexen-4-yne by ab initio and hybrid DFT methods
Energy differences/cmꢀ1
Gaucheb
a
Method/basis
Energy/Eh
Cis
HF/6-31G(d)
HF/6-311G(d)
ꢀ231.784581
ꢀ231.829430
ꢀ231.854390
ꢀ232.570722
ꢀ232.795729
ꢀ232.862611
ꢀ233.368123
ꢀ233.435043
ꢀ233.444629
ꢀ52
ꢀ72
ꢀ29
95
HF/6-311G(2d,2p)
MP2(full)/6-31G(d)
MP2(full)/6-311G(d,p)
MP2(full)/6-311G(2d,2p)
B3LYP/6-31G(d)
47
242
115
80
B3LYP/6-311G(d,p)
B3LYP/6-311G(2d,2p)
87
a
b
The energy units are hartree. The negative sign indicates that the
gauche conformer is more stable.
Fig. 4 Raman spectra of 1-hexen-4-yne: (A) liquid; and (B) polycrys-
talline solid.
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551
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Table 2 Structural parametersa for cis and gauche conformers of 1-hexen-4-yne from ab initio calculations
RHF/6-31G(d)
MP2/6-31G(d)
MP2/6-311G(d,p)
Cis Gauche
MP2/6-311G(2d,2p)
Cis Gauche
1.332
b
Parameters
Cis
Gauche
1.317
Cis
Gauche
1.336
r(C1–C2)
r(C2–C3)
r(C3–C4)
Q
R1
R2
L
1.317
1.511
1.471
1.188
1.469
1.075
1.075
1.079
1.088
1.088
1.084
1.084
1.084
126.8
115.4
180.0
122.0
120.9
119.3
117.0
113.8
108.9
108.9
110.7
108.1
108.1
0.0
1.335
1.509
1.462
1.221
1.462
1.085
1.084
1.089
1.099
1.099
1.094
1.093
1.093
125.4
114.4
180.0
121.4
121.1
119.7
177.5
114.9
109.5
109.5
110.9
107.9
107.9
0.0
1.337
1.511
1.461
1.219
1.462
1.085
1.084
1.089
1.098
1.098
1.093
1.093
1.093
1.337
1.507
1.466
1.219
1.462
1.086
1.084
1.088
1.098
1.096
1.093
1.093
1.093
1.331
1.507
1.460
1.214
1.461
1.079
1.078
1.082
1.091
1.091
1.086
1.086
1.086
1.510
1.475
1.188
1.469
1.077
1.075
1.078
1.088
1.085
1.084
1.084
1.084
1.505
1.466
1.221
1.461
1.086
1.085
1.089
1.099
1.097
1.094
1.094
1.094
1.504
1.465
1.214
1.461
1.080
1.078
1.082
1.090
1.089
1.086
1.086
1.086
=
r(C C)
=
r(C10–C11
r(C1–H5)
r(C1–H6)
r(C2–H7)
r(C3–H8)
r(C3–H9)
)
R3
r1
r2
r3
r4
r5
r(C11–H12
r(C11–H13
r(C11–H14
)
)
)
r6
r7
r8
cC1C2C3
cC2C3C4
cC3C4C10
cC2C1H5
cC2C1H6
cC1C2H7
cH5C1H6
cH7C2C3
cC4C3H8
cC4C3H9
cH12C11C10
cH13C11H12
cH14C11H12
tC1C2C3C4
tH5C1C2H3
tH5C1C2H6
tH7C2C1C3
tH8C3C4C2
tH9C3C4C2
tC2C3C10H12
tH13C11H12C10
tH14C11H12C10
A
b1
f
124.5
123.9
125.3
123.7
125.1
123.8
112.5
180.0
121.9
121.5
119.8
116.5
115.6
108.5
109.5
110.7
108.1
108.2
125.2
ꢀ1.0
111.9
180.0
121.6
121.6
120.1
116.8
116.0
109.2
110.0
111.0
107.8
107.9
123.3
ꢀ0.5
114.5
180.0
121.0
120.8
119.6
118.2
115.0
109.3
109.3
110.8
108.1
108.1
0.0
111.9
180.0
121.1
121.3
120.2
117.5
116.1
109.0
109.8
110.8
108.0
108.1
121.7
ꢀ0.3
114.1
180.0
120.8
120.9
119.5
118.3
115.3
109.4
109.4
110.9
108.0
108.0
0.0
111.9
180.0
121.0
121.3
119.9
117.6
116.3
108.9
110.0
110.9
108.0
108.0
122.3
ꢀ0.3
j1
a2
a3
b3
a1
b2
e1
e2
d1
g1
g2
t1
S
0.0
0.0
0.0
0.0
S
D2
180.0
180.0
ꢀ122.6
122.6
180.0
121.5
ꢀ121.5
8814.4
1736.6
1476.8
0.231
0.123
0.000
0.261
0.784581
52
180.2
180.0.5
180.0
180.0
ꢀ122.5
122.5
180.0
121.8
ꢀ121.8
8628.0
1754.8
1484.9
0.254
0.115
0.000
0.278
1.570722
180.2
179.9
ꢀ121.5
121.9
ꢀ9.4
180.0
180.0
ꢀ122.3
122.3
180.0
121.6
ꢀ121.6
8632.8
1754.2
1484.8
180.2
179.6
ꢀ121.2
121.8
ꢀ20.0
121.5
ꢀ121.7
13026.1
1374.7
1309.2
180.0
180.0
ꢀ122.3
122.3
180.0
121.7
ꢀ121.7
8677.0
1770.2
1497.1
180.1
179.6
ꢀ121.3
121.8
ꢀ12.6
121.6
ꢀ121.8
13187.0
1379.0
1313.5
ꢀ121.2
122.6
ꢀ10.6
121.4
121.8
ꢀ121.9
13217.7
1369.2
1304.8
ꢀ121.6
13699.5
1369.2
1306.4
B
C
|ma|
|mb|
|mc|
|mt|
0.242
0.017
0.256
0.010
0.290
0.121
0.328
0.015
0.282
0.146
0.325
0.032
0.082
0.256
0.784819
0.080
0.268
1.5702868
0.000
0.314
1.795729
0.064
0.334
1.795511
0.000
0.317
1.862611
0.067
0.333
1.861503
ꢀ(E + 231)
DE/cmꢀ1
95
47
242
a
b
Bond distances in A, angles in degrees, rotational constants in MHz, dipole moments in Debye, and energies in Hartree. Internal coordinates.
˚
transformed to normal coordinates by:
ꢀ
ꢁ
ꢀ
ꢁ
X
@mu
@Qi
@mu
@Xj
¼
Lij
j
where the Qi is the ith normal coordinate, Xj is the jth Carte-
sian displacement coordinate and Lij is the transformation
matrix between the Cartesian displacement coordinates and
normal coordinates. The infrared intensities were then calcu-
lated by:
"
#
ꢀ
ꢁ
2þ
ꢀ
ꢁ
2þ
ꢀ
ꢁ
2
@my
@Qi
Np @mx
@mz
@Qi
Ii ¼
:
3c2
@Qi
The predicted spectra of the pure gauche and cis conformers
are shown in Figs. 2C and 2D, respectively. The predicted
spectrum of the mixture of both forms utilizing the experimen-
tal DH value of 233 cmꢀ1 is shown in Fig. 2B which is in good
agreement with the experimental spectrum of the sample
Fig. 5 Internal coordinates for 1-hexen-4-yne.
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Phys. Chem. Chem. Phys., 2003, 5, 2541–2551
2545

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Nevertheless, the agreement between the calculated and
observed spectra shows how useful the ab initio predictions
can be for making the vibrational assignment for the indivi-
dual conformers.
Vibrational assignment
The cis conformer of 1-hexen-4-yne has CS symmetry and the
fundamental vibrations span the irreducible representations
25A0 + 11A00. The ab initio calculations show that the C princi-
pal axis of the cis conformer is perpendicular to the symmetry
plane (Table 2). Therefore, the out-of-plane modes are
expected to give rise to C-type band contours in the infrared
spectrum and yield depolarized lines in the Raman spectrum.
For the gauche conformer, the band contours can be A-, B-,
and C-type or any hybrid combination because this form has
only trivial C1 symmetry. Therefore, the vibrational assign-
ment is based on the predicted frequencies, infrared intensities,
Raman activities as well as depolarization ratios, and infrared
band contours from ab initio calculations.
The Raman lines at 1295, 1220, 1142, 785, 604 and 271 cmꢀ1
in the spectrum of liquid disappear from the Raman spectrum
of the well annealed polycrystalline solid. Similarly, the infra-
red bands at 1284, 1266, 1220, 1031, 935, 783, 602 and 460
cmꢀ1 in the spectrum from the krypton solution are absent
in the spectrum of the solid. According to the ab initio predic-
tions, all of these bands arise from the fundamentals of the
gauche conformer. Therefore, it is clear that the cis conformer
is the only conformer present in the annealed polycrystalline
solid and all of the bands in the infrared and Raman spectra
of the solid are assigned to this conformer.
Fig. 6 Raman spectra of 1-hexen-4-yne: (A) liquid; (B) simulated
infrared spectrum of the cis and gauche conformer mixture with the
DH of 233 cmꢀ1 at 25 ꢁC; (C) calculated spectrum of the pure gauche
conformer; and (D) calculated spectrum of the pure cis conformer.
The carbon–hydrogen modes of the cis conformer were
assigned straightforwardly. The ab initio calculations predicted
=
that the CH2 antisymmetric and symmetric stretches have the
highest and the second highest frequencies. Thus the two peaks
at 3091 and 3058 cmꢀ1 are assigned to these two fundamentals.
A series of Q-branches with strong, weak, weak, strong, etc.,
intensity pattern are observed in the infrared spectrum of the
gas which are due to the carbon–hydrogen stretches of a nearly
free internal rotation of the methyl group. Based on the inten-
sities, the K ¼ 0 branch must be either the band at 3007 or
2978 cmꢀ1; the latter is more acceptable because it is consistent
with the intensity pattern of the infrared spectrum of the kryp-
ton solution. Therefore, this peak is confidently assigned to the
CH3 antisymmetric stretches. The two CH3 antisymmetric
deformations (n9 , n26) are almost degenerate and assigned at
1453 cmꢀ1 as the band center which is between the two stron-
gest Q branches in the infrared spectrum of the gas. These near
degenerate fundamentals shift and split as the two CH3 defor-
mations at 1441 and 1436 cmꢀ1 in the infrared spectrum of the
polycrystalline solid. In the study of another similar molecule,
1-penten-4-yne,16 the CH2 deformation, wag and twist funda-
mentals of the cis conformer were assigned at 1400, 1324 and
1208 cmꢀ1, respectively, in the infrared spectrum of the solid.
Because of the similarity between these two molecules and by
using the ‘‘group frequency’’ principle, the corresponding fun-
damentals of cis 1-hexen-4-yne are assigned at 1399, 1324 and
1212 cmꢀ1, respectively, in the infrared spectrum of the solid.
The carbon–hydrogen modes arising from the gauche con-
former can be readily assigned by comparing the spectra from
the fluid phases with that from the polycrystalline solid state
where those disappearing from the spectra of the gas or liquid
must rise from the gauche conformer. It should be noted that
all of the assignments for these bands are consistent with the
predicted frequencies from the ab initio calculations. For
example, according to ab initio MP2/6-31G(d) calculations,
the CH2 twists are expected at 1215 and 1198 cmꢀ1 for the
gauche and cis conformers, respectively, with the infrared
intensities of 0.6 and 1.6 km molꢀ1. Therefore, the n027 where
the prime indicates a mode of the less stable gauche form and
dissolved in liquid krypton (Fig. 2A) at the temperature of
ꢀ125 ꢁC. However, there exist some notable differences. For
example, the simulated peak about 1020 cmꢀ1 is stronger than
the corresponding one in the experimental spectrum.
The simulated Raman spectra are shown in Fig. 6. The fre-
quencies and Raman scattering activities were obtained from
the ab initio MP2/6-31G(d) calculations. The Raman activities
were determined by using the previously developed22,23 analy-
tical gradient method. The activity Sj can be expressed as:
Sj ¼ gj ð45 a2j þ 7 bj2Þ
where gj is the degeneracy of the vibrational mode j and aj
is the derivative of the isotropic polarizability, and bj is that
of the anisotropic polarizability. The Raman scattering cross
sections, @sj/@O, which are proportional to the Raman
intensities, can be calculated from the predicted scaled
wavenumbers for each mode.24,25 To obtain the polarized
Raman cross sections, the polarizabilities are incorporated
into Sj by Sj [(1 ꢀ rj)/(1 + rj)], where rj is the depolarization
ratio of the jth normal mode. The Raman scattering cross sec-
tions and the calculated wavenumbers were used together with
a Lorentzian function to obtain the calculated spectra.
The predicted Raman spectra of the pure cis and gauche
conformers of 1-hexen-4-yne are shown in Figs. 6D and 6C,
respectively. The predicted Raman spectrum of the mixture
of the two conformers at 25 ꢁC, with an enthalpy difference
of 233 cmꢀ1 with the cis conformer the more stable conformer,
is shown in Fig. 6B. There are several differences existing
between the predicted and experimental spectra. The simulated
spectrum (Fig. 6B) gives poor predictions for the intensities of
the n8 and n32 fundamentals at 1647 and 562 cmꢀ1, respec-
tively, and the frequency of the n33 fundamental is poorly
predicted at 277 cmꢀ1 whereas it is observed at 368 cmꢀ1
.
2546 Phys. Chem. Chem. Phys., 2003, 5, 2541–2551

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n27 fundamentals were assigned to the infrared bands at 1220
and 1210 cmꢀ1, respectively, where the weaker band at 1220
cmꢀ1 disappears from the spectrum of the amorphous solid
with annealing.
=
The C CC bend (n21) of the cis conformer is expected at 378
cmꢀ1 with a Raman activity of 4.2 A u (Table 3) and the
lines at 397 and 400 cmꢀ1 with the medium intensities in
the Raman spectra of the liquid and solid, respectively, are
assigned to this fundamental. The C2C3C4 bends (n20 and
n020) are assigned to the lines at 561 and 458 cmꢀ1 to the cis
and gauche conformers, respectively, in the infrared spectrum
of the gas whereas the latter is absent from the spectrum of
the well annealed polycrystalline solid. Similarly, the C2C3
stretch can be assigned to an infrared peak at 904 cmꢀ1 in
the infrared spectrum of the solid to the cis from.
4
ꢀ1
˚
The most interesting part of the spectrum is the far infrared
=
region where the C CC in-plane and out-of-plane bends as
=
well as the asymmetric torsion are found. Similar to those of
2-hexyne,26 2-pentyne27 and 1-penten-4-yne,16 the predicted
frequency of the C3C4C10 out-of-plane bend (n33) from
MP2/6-31G(d) calculations is always lower than the observed
frequency. Therefore, the n33 fundamental of the cis conformer
is assigned to lines at 368 and 373 cmꢀ1 in the Raman spectra
of the liquid and the polycrystalline solid, respectively, which is
about 100 cmꢀ1 higher than the ab initio predicted value. The
contour of the C3C4C10 in-plane bend of the gauche conformer
(n023) is predicted to be a hybrid of 57% B- and 42% C-type.
Therefore, the band centered at 97 cmꢀ1 with a clear Q-branch
is assigned to this fundamental. The asymmetric torsion of the
cis conformer, which is predicted to have a pure C-type con-
tour, is assigned at 123 cmꢀ1. The n22 and n23 in-plane bending
modes of the cis conformer are assigned to the peaks at 284
and 115 cmꢀ1, respectively, in the infrared spectrum of the
gas whereas n34 , the C4C10C11 out-of-plane bend is observed
at 230 cmꢀ1. The complete assignment of the observed funda-
mentals for both cis and gauche conformers of 1-hexen-4-yne is
given in Table S1.y
Fig. 7 Mid-infrared spectra of 1-hexen-4-yne (500 to 1250 cmꢀ1): (A)
dissolved in liquid krypton at ꢀ125 ꢁC and (B) polycrystalline solid.
the vapor state28–32 since the two conformers have similar
molecular volumes and dipole moments which differ by less
than 5%. With this enthalpy difference, the estimated abun-
dance of the gauche conformers is 39 ꢂ 2% at ambient
temperature.
Coriolis interaction
In the infrared spectrum of gaseous 1-hexen-4-yne, a series of
strong, weak, weak strong, etc. alternations of Q-branches
(Fig. 9) were observed. This spectrum pattern is typical of per-
pendicular bands of symmetric top molecules such as methyl
halides. For a symmetric top molecule, the overall rotational
motions of the molecule interact with the angular momentum
of the E vibration of the methyl group which causes the split-
ting of the degenerate E modes. In 1-hexen-4-yne, as the
Conformational stability
By comparing the vibrational spectra from the fluid states with
that from the well annealed solid, many bands are found to
disappear from the spectrum of the solid and as mentioned
earlier, it includes six Raman lines and eight infrared bands.
Based on the ab initio predictions, all of those bands are
assigned to the gauche conformer. Therefore, many conformer
pairs could be identified (Fig. 7) in the krypton solution and
seven conformer pairs were used to determine the enthalpy
difference between the cis and gauche conformers.
The spectral changes of the krypton solution were recorded
as functions of temperature from ꢀ105 ꢁC to ꢀ150 ꢁC. The
conformer pair 1210/1111 cmꢀ1 (Fig. 8) where the first one
arises from the cis conformer clearly shows the increased inten-
sity of the cis conformer as the temperature decreases which is
consistent with the ab initio MP2 calculations. The enthalpy
difference was calculated by the van’t Hoff equation lnk ¼
(DH/RT ) ꢀ DS/R with the assumption that the value of DH
is a constant within the utilized temperature range. By using
the least squares fit and the slope of the lines, the values of
DH range from a high value of 293 ꢂ 15 cmꢀ1 to a low value
of 176 ꢂ 8 cmꢀ1 with the cis conformer the more stable form
(Table 4) with an average of 233 ꢂ 6 cmꢀ1 (2.79 ꢂ 0.07 kJ
molꢀ1). The statistical uncertainty of these values does not
take into consideration the potential interferences from the
overtones and combination bands near coincidence to the fun-
damentals which were used for the enthalpy determination.
Therefore, a more realistic value for the uncertainty should
be at least ten percent which results in an average value of
233 ꢂ 23 cmꢀ1 (2.79 ꢂ 0.28 kJ molꢀ1) for the enthalpy differ-
ence. This enthalpy difference should be close to the value in
Fig. 8 Temperature dependent infrared spectrum of 1-hexen-4-yne in
liquid krypton for the cis (1210 cmꢀ1) and the gauche (1111 cmꢀ1) in
the temperature range from ꢀ105 to ꢀ145 ꢁC.
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551
2547

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Table 4 Temperature and intensity ratios for the conformational study of 1-hexen-4-yne dissolved in krypton solutiona
T/ꢁC
1000/K
I1210/1111
I1210/898
I1210/783
I558/898
I1048/1111
I1048/898
I558/1111
ꢀ105
ꢀ110
ꢀ115
ꢀ125
ꢀ130
ꢀ135
ꢀ140
ꢀ145
ꢀ150
DH/cmꢀ1
5.9471
6.1293
6.3231
6.7499
6.9857
7.2385
7.5103
7.8033
8.1202
0.4552
0.5398
0.5847
0.6839
0.7222
0.7990
0.8720
0.9348
1.1524
265 ꢂ 13
0.4663
0.4808
0.5125
0.5882
0.6236
0.6751
0.7471
0.8256
0.9412
224 ꢂ 6
0.7241
0.7740
0.8072
0.9494
0.9868
1.0673
1.1622
1.2226
1.3974
203 ꢂ 5
—
1.4236
1.7438
1.8963
2.2680
2.4563
2.7250
2.9746
3.2615
3.9253
293 ꢂ 15
1.4585
1.5534
1.6623
1.9505
2.1209
2.3024
2.5484
2.8532
3.2061
251 ꢂ 1
9.9310
11.4107
12.1172
13.4842
14.1329
15.1512
16.5169
17.4504
20.7781
207 ꢂ 11
10.1651
10.6125
11.5964
12.2032
12.8020
14.1502
15.2659
16.9713
176 ꢂ 8
Average DH ¼ 233 ꢂ 6 cmꢀ1(2.79 ꢂ 0.07 kJ molꢀ1)with the cis conformer more stable.
a
methyl group at the end of the triple bond is a nearly free rotor
with a torsional barrier of 100 cmꢀ1 predicted by the MP2/6-
31G(d) calculations, one expects the same sub-band structure
will be observed. Similar sub-band structures have been
reported for 2-hexyne,26 2-pentyne,27 5-halo-2-pentynes33,34
and the 1-halo-2-butynes35,36 which are not symmetric top
molecules. The frequencies of the Q-branches of the different
sub-bands agree well with the formula ns0ub ¼ c0 ꢂ c1m + c2m2.
For a perpendicular band of a symmetric-top molecule such
as the degenerate fundamentals of a methyl group, the formula
for the sub-band structure with the type of intensity alterna-
tion already mentioned has been given by37,38
angular momentum of the pseudo-degenerate vibrations with
the internal rotational angular momentum of the almost freely
rotating internal top and not with the overall rotation of the
molecule. A quadratic equation can be derived from first prin-
ciples using the appropriate Hamiltonian, but in order to
retain the z notation, the following equation can be derived
from the sub-band formula for overall rotation of symmetric
top molecules by elimination of the kinetic constants for over-
all rotation, B or (B + C)/2, and by replacing the A constants
with F1 which is h/8p2cItred, the inverse reduced moment of
inertia for internal rotation of the methyl top in the slightly
asymmetric top molecule
2
2
ns0ub ¼ n0 þ ½A0ð1 ꢀ zÞ ꢀ B0ꢅ ꢂ 2½A0ð1 ꢀ zÞ ꢀ B0ꢅK
ns0ub ¼ ½n0 þ F0 ð1 ꢀ zÞ ꢅ þ 2F0 ð1 ꢀ zÞm þ ðF01 ꢀ F001Þm2:
1
1
þ ½ðA0 ꢀ B0Þ ꢀ ðA00 ꢀ B00ÞꢅK2
where z is the Coriolis coupling constant and the factor (1 ꢀ z)2
is used rather than (1 ꢀ 2z) as given by Herzberg39 and
Nyquist.40 The single prime refers to the upper state and
double prime to the lower state.
For 1-hexen-4-yne, the cis conformer is more nearly a sym-
metric top than the gauche conformer. The sub-band structure
probably arises from the near degeneracy of n4/n24 and n9/n26
of the cis form. Values for the kinetic constant F00 in the
1
ground vibrational state are obtained from ab initio optimized
geometric structures of the cis conformer given in Table 2. The
frequencies of the observed sub-bands are listed in Table 5.
Fits to the sub-band peaks have been made by the least-
squares method for the formula ns0ub ¼ c0 ꢂ c1m + c2m2 and
the values for coefficients are given in Table 5. For each of
the bands, the quadratic coefficient c2 is small where it is the
change in the internal rotational constant, F, between the
ground and excited states. For the CH3 nearly-degenerate
stretching fundamentals, n4/n24 , by taking F00 ¼ 5.6 cmꢀ1
from the ab initio calculation, one obtains z ¼ 0.129 ꢂ 0.002
from the coefficient of the linear term, 2F0(1 ꢀ z), and from
n0 + F0(1 ꢀ z)2 the band center, is determined to have a value
However, for 1-hexen-4-yne and other similar molecules, the
sub-band structure is due to the interaction of the vibrational
of 2973.7 cmꢀ1
.
For the CH3 deformational fundamentals, n9/n26 , the center
of the sub-band series is more difficult to determine since the
series has an interval of 22 cmꢀ1 instead of 14 cmꢀ1. Therefore
only the more obvious parts were used to obtain z ¼
ꢀ0.221 ꢂ 0.05 from the linear term and the band origin, n0 ,
is 1453.4 cmꢀ1 and the results are listed in Table 5.
Discussion
By utilizing seven conformer pairs from the temperature
dependent study of the infrared spectra with the sample
dissolved in krypton solution, the enthalpy difference of
233 ꢂ 23 cmꢀ1 (2.79 ꢂ 0.28 kJ molꢀ1) was obtained with the
cis form the more stable rotamer. This result is in agreement
with the predicted value of 242 cmꢀ1 from the MP2/6-
311G(2d, 2p) calculations. Because of the nearly free rotation
of the methyl group, diffuse functions were not added to the
basis sets for the ab initio calculations since they make it
almost impossible to converge. However, all of the Hartree–
Fock calculations give the wrong conformer stability
Fig. 9 Sub-band structure in the degenerate: (A) CH3 antisymmetric
stretching band due to Coriolis interaction and (B) CH3 antisymmetric
deformation band due to Coriolis interaction.
2548
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551

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Table 5 Coriolis structure of nearly-degenerate CH3 antisymmetric
stretching and deformation bands of 1-hexen-4-yne
doubtful that either a microwave or electron diffraction study
could verify these differences in the structural parameters of
the two conformers. However, either study would be of interest
for the determination of the heavy atom distances for compar-
ison with the ab initio MP2/6-311G(d, p) predicted values.
It is interesting to compare the structural parameters
between 1-hexen-4-yne and 1-penten-4-yne16 where the only
difference is the substitution of the methyl group of the former
molecule with a hydrogen atom. The structural parameters are
essentially the same for the two molecules according to the
=
CH3 antisymmetric
stretch
CH3 antisymmetric
deformation
m
nobs
nobs ꢀ ncalc nobs
nobs ꢀ ncalc
10
9
8
7
6
5
4
3
2
1
0
3073.52
3064.08
3054.19
3044.59
3035.16
3025.46
3016.66
3007.05
2997.60
2987.92
2978.60
2968.61
2958.32
2947.86
0.64
0.24
0.25
ꢀ0.08
0.11
ab initio MP2/6-31G(d) calculations. For example, the C C
=
˚
bond distance is predicted to be only 0.002 A longer for 1-
hexen-4-yne than the corresponding bond of 1-penten-4-
=
yne and the C C bond distances are predicted to have the
1541.92
1527.59
1514.24
1501.24
0.96
ꢀ0.62
0.41
ꢀ0.40
ꢀ0.62
ꢀ0.40
ꢀ0.43
ꢀ0.23
0.31
same values. Based on essentially the same values of the struc-
tural parameters, one expects that the conformational stability
values should be the same which is confirmed by the enthalpy
differences of 233 ꢂ 23 cmꢀ1 and 248 ꢂ 25 cmꢀ1 for 1-hexen-4-
yne and 1-penten-4-yne, respectively, from the krypton solu-
tions. Therefore, the substitution of hydrogen by a methyl
group for 1-hexen-4-yne does not have a significant effect on
either the structural parameters or conformational behavior.
Because the methyl group is a nearly free internal rotor, two
sub-band structures are observed in the infrared spectrum of
the gas. The experiment determined values of z are 0.129 and
ꢀ0.221 for the CH3 stretch and deformational modes and
these values are consistent with the corresponding ones for
the overall rotation of the methyl halides.39 These results
clearly indicate that the rotational barrier of the methyl group
is very small. However, this internal rotational fine-structure is
not observed for the CH3 rocking modes. This observation is
probably due to the barrier of 100 cmꢀ1 as predicted by the
MP2/6-31G(d) calculations. This value is much larger than
the methyl barrier value of other similar molecules such as
dimethylacetylene41 which is only about 6 cmꢀ1. Additionally,
most of the Q-branches for CH3 deformation are split which
further suggests a relatively small but a significant value of
the barrier.
1474.57
1461.34
1447.60
1434.31
1420.89
1406.84
ꢀ0.32
ꢀ0.01
ꢀ0.11
0.35
0.44
0.40
ꢀ1
ꢀ2
ꢀ0.08
ꢀ0.70
ꢀ3
0.79
0.71
ꢀ4
ꢀ5
ꢀ6
1377.21
1363.26
1349.04
1334.54
1320.41
ꢀ0.67
ꢀ0.33
ꢀ0.16
ꢀ0.16
0.32
ꢀ7
ꢀ8
ꢀ9
ꢀ10
Standard deviation
0.46
ꢂ0.1646
0.55
c0
c1
c2
z
2977.96
1461.35
ꢂ0.207
9.7355 ꢂ0.0663
13.590 ꢂ0.038
ꢀ0.054 ꢂ0.006
ꢀ0.221 ꢂ0.005
ꢀ0.0223 ꢂ0.0084
0.129
2973.72
ꢂ0.003
ꢂ0.13
n0
1453.05
ꢂ0.27
predictions with the gauche conformer more stable by 29 to 52
cmꢀ1. Although the DFT calculations give the correct predic-
tions for the conformational stability, they provide poor values
for the energy difference compared to the experimental value.
Therefore, the electron correlation with a relatively large basis
set must be employed to obtain reasonable results from the
ab initio calculations for these unsaturated carbon–hydrogen
compounds such as 1-hexen-4-yne. Nevertheless a theoretical
prediction should be confirmed with experimental results.
In order to obtain better predicted frequencies, three scaling
factors were utilized for the force constants with the MP2/6-
31G(d) calculations which were 0.88 for C–H stretches, 0.9
for the C–H bends and heavy atom stretches, and 1.3 for the
Most of the diagonal force constants have similar values
between the two conformers with only a few exceptions. The
force constants for the C3C4 and C3H9 stretches are larger
by 1.6% and 1.4%, respectively, for the cis conformer. How-
ever, the largest difference among force constants arises from
the C2C3C4 bend (f) which is about 35% larger for the cis rota-
mer than that of gauche form. This is probably due to the
significant differences in the C2C3 and C3C4 bond distances
between the two conformers along with the angle difference
which results in a rather larger frequency difference in the
two fundamentals. Therefore, the C2C3C4 bends (n20 , n0
)
20
=
C CC in-plane and out-of-plane bending modes while keeping
=
of the cis and gauche conformers are observed at 561 and
460 cmꢀ1, respectively, in the infrared spectrum of krypton
solution. The force constants of the C1C2C3 and C3C2H7 bends
are also larger for the cis form than those of the gauche confor-
mer by 18 and 7.9%, respectively. Another significant differ-
ence in force constants is found for the asymmetric torsion
with the value larger by 12.5% for the cis form. Additionally,
the force constants for the H8C3C9 bend (s), CH in-plane bend
(S1) and C3C2H7 out-of-plane bend (o2) are larger by 5%, 4%
and 6.5%, respectively, than their corresponding ones of the
gauche conformer. Therefore, the skeleton modes have the
most significant differences in their frequencies for the two
conformers.
the rest of the force constants unscaled. It should be noted that
=
the MP2 calculations give poor predictions for the C CC
=
out-of-plane modes for both conformers even with the scaling
factor of 1.3. However, the B3LYP/6-31G(d) calculations pro-
vide much more accurate predictions for these modes (Table 3)
and the correct assignment of these low frequency modes
usually requires DFT calculations. The difference between
the observed and scaled MP2/6-31G(d) predicted frequencies
is 18 cmꢀ1 for the fundamentals of the cis conformer which
represents an average error of 1.3%.
For 1-hexen-4-yne, the structural parameters are nearly the
same for the cis and gauche conformers except the C2C3 and
C3C4 distances and C1C2C3 and C2C3C4 angles. The cis con-
The potential energy distributions (P.E.D.) are relatively
pure for the cis conformer compared to those for the gauche
conformer (Table 3). Nevertheless there are still several funda-
mentals which are significantly mixed, especially some skeletal
modes for the cis form. The C2C3C4 bend and the C3C4 and
C10C11 stretches (n20 , n19 and n15) have only 19, 16, and 36%
of contributions from the described motions. Other modes
=
˚
former C2C3 and C3C9 bond distances are 0.004 and 0.002 A
longer than those of the gauche form whereas the C3C4 bond
˚
distance is 0.004 A shorter for the cis form. The C1C2C3 and
C2C3C4 angles in the cis form are 1.5 and 2.5ꢁ, respectively,
larger than their counterparts in the gauche conformer. Addi-
tionally, the H7C2C3 angle of the gauche conformer is 1.1ꢁ lar-
ger than the corresponding value of the cis conformer. It is
including C CC and C4C10C11 out-of-plane bends (n21 ,n34
)
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551
2549

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Table 6 Potential barriers (cmꢀ1) and coefficients (cmꢀ1) of 1-hexen-
4-yne determined from far infrared spectra
Coefficients
Experimentala
MP2/6-31G(d)
V1
V2
86 ꢂ 3
212 ꢂ 2
578 ꢂ 2
47 ꢂ 2
—
ꢀ6
175
821
ꢀ25
—
V3
V4
V5
V6
DH/cmꢀ1
—
233 ꢂ 23
ꢀ46
Potential barriers
Cis ! gauche
798
405
931
810
Gauche ! gauche
Gauche ! cis
538
121.7b
836
123.3
Dihedral angle
a
Calculated using: F0 ¼ 1.657861, F1 ¼ 0.435616, F2 ¼ 0.292670,
Fig. 10 Potential function governing the internal rotation of 1-
hexen-4-yne as determined by ab initio calculations (dotted line,
MP2/6-31(d)) and from spectral data (solid line).
F3 ¼ 0.067047, F4 ¼ 0.035545, F5 ¼ 0.0090684, F6 ¼ 0.004549 cmꢀ1
.
b
From MP2/6-311G(d, p) calculation.
agreement with the experimental values. However, the pre-
dicted value of the V1 term is quite small mainly because of
the small predicted energy difference between the conformers.
The torsional potential functions from both ab initio and
experimental fitting are shown in Fig. 10. For the experimen-
tally determined function, the values of the cis to gauche,
gauche to cis and gauche to gauche barriers are 816, 577 and
384 cmꢀ1, respectively. All of these values are smaller than
those of the predicted ones (Table 6) with the gauche to gauche
barrier appearing to be too small since only one torsional tran-
sition was observed for the gauche conformer, the gauche to
gauche barrier has a rather larger uncertainty with the
predicted one being considered more reasonable.
have contributions of less than 50% as the major contributions
to the fundamentals. The mixing is more extensive for the
gauche conformer where, for example, the C3C4 stretch (n019
)
has only 14% contributions from this described motion. Thus,
the description given for the normal modes of the gauche con-
former are more for bookkeeping than to give an accurate
account of atom displacements in the molecule.
The potential function governing the conformer interconver-
sion was obtained by utilizing the experimental enthalpy value,
observed torsional transition fundamental frequencies and the
dihedral angle from the ab initio calculation (Table 6). The
torsional potential is represented by a Fourier cosine series
in the internal rotation angle f
=
The Fermi resonance should be noted for the C C stretch
=
ꢀ
ꢁ
6
X
Vi
(2302 and 2247 cmꢀ1) where the higher frequency line is only
slightly less intense than the 2247 cmꢀ1 in the Raman spectrum
of the solid (Fig. 4). This doublet arises from the overtone of
the carbon–carbon stretch (n15) of the methyl group on the
triple bond. Such a doublet is not observed in the spectrum
of 1-penten-4-yne16 but is observed in other molecules where
the triple bond has a methyl group attached.
VðfÞ ¼
ð1 ꢀ cos i fÞ
2
i¼1
where f and i are the torsional angle and foldness of the bar-
rier, respectively. The internal rotation constant F(f), which is
used to calculate the potential function, also varies as a func-
tion of the internal rotation angle, and this is approximated
by another Fourier series
Both the MP2/6-311G(d,p) and MP2/6-311G(2p,2d) calcu-
lations gave the correct predictions for the conformer stability
for 1-hexen-4-yne, but the former one gave a very low pre-
dicted energy difference of 47 cmꢀ1 compared with the experi-
mentally determined enthalpy value of 233 ꢂ 23 cmꢀ1. The
5
X
FðfÞ ¼ F0 þ
Fi cos i f:
ꢀ
i ¼1
˚
The relaxation of the structural parameters, B(f), during the
internal rotation can be incorporated into the above equation
by assuming them to be small periodic functions of the
torsional angle of the general type
predicted triple bond distance of 1.219 A from the calculations
which utilized a single set of polarization functions is a value
which is significantly larger than the corresponding values
(both conformers) from the calculations with a double set of
polarization functions. These predicted values are undoubtedly
BðfÞ ¼ a þ b cosf þ c sinf
˚
˚
too long by at least 0.010 A and probably as much as 0.015 A.
=
Three peaks were observed in the far infrared spectrum of
the gas which are assigned to the torsional transitions of this
molecule. The peaks at 123.8 and 117.0 cmꢀ1 are assigned to
the 1 0 and 2 1 transitions of the cis conformer and the
peak at 73.0 cmꢀ1 is assigned to the1 0 transition of the
gauche conformer. By utilizing these experimental data along
with the determined enthalpy value and the predicted dihedral
angle, the V1 , V2 , V3 and V4 potential terms were obtained.
Their values along with the statistical uncertainties are listed
in Table 6. The uncertainties for the V1 to V3 terms are
undoubtedly too small where one for the V2 term should be
more like ꢂ20 cmꢀ1 with a similar uncertainty for the V3 term.
For the purpose of comparison, the calculated potential func-
tion was generated by the MP2/6-31G(d) calculations. The
predicted values of the V2 and V3 terms are in reasonable
In fact, the C C distance varies very little with changes of sub-
=
stituents and falls in the range 1.200 to 1.210 A where the
˚
longer value has been reported42 for 1-pentyne. For the similar
molecule, 1-penten-4-yne, the MP2/6-311+G(d,p) calculations
not only gave a longer value for the triple bond distance than
that obtained from the MP2/6-311+G(2d,2p) calculations but
it also gave a wrong prediction for the conformational stabi-
lity. Therefore, in order to obtain a reasonably predicted
=
C C distance and conformational stability, the ab initio MP2
=
calculations require a rather larger basis set and double polar-
ization functions. This is quite different with hybrid DFT cal-
culations by the B3LYP method which provides a reasonable
˚
value of 1.203 A for the triple bond distances for the two
conformers of 1-hexen-4-yne with only the small 6-31G(d)
basis set and this band distance is predicted to be shorter at
2550
Phys. Chem. Chem. Phys., 2003, 5, 2541–2551

View Article Online
˚
1.200 A with the 6-311G(d,p) basis set. However, the predicted
19 Gaussian 98 (Revision A.7) M. J. Frisch, G. W. Trucks, H. B.
Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G.
Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C.
Burant, S. Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin,
M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R.
Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J.
Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma,
D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman,
J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P.
Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T.
Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C.
Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen,
M. W. Wong, J. L. Andres, C. Gonzalez, M. Head-Gordon, E. S.
Replogle and J. A. Pople, Gaussian Inc., Pittsburgh PA, 1998.
20 P. Pulay, Mol. Phys., 1969, 17, 197.
energy differences from the DFT calculations are quite poor
with the values ranging from 115 cmꢀ1 with the small basis
set to only 87 cmꢀ1 with the larger one (Table 1). Nevertheless,
the DFT calculations predicted excellent frequencies for the
=
=
=
C CH and C CCH bending fundamentals and such calcula-
=
3
tions are essential for the correct assignment of these skeletal
modes for compounds with the triple bond.
Acknowledgements
JRD acknowledges the University of Missouri-Kansas City for
a Faculty Research grant for partial financial support of this
research.
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